Africa and the cold beauty of Maths

Better still, the boundaries of ignorance get pushed backwards, which is always a good idea, and a fine Christmas present.

From the isolation of my study, and from the depths of my ignorance, I had always bemoaned the fact that poorer countries, particularly in Africa, avoided taking part in PISA and similar international assessments. The suspicion was that they were avoiding getting bad results, which would redound on their national pride, showing them to be dull and/or incapable of organising their schools properly. PISA has the capacity to spread embarrassment far and wide, in rich as well as poor countries, and I am all in favour of that. Let the over-paid educational authorities of the rich world be confounded by the wit of poorer nations, and may their cosy empires fall. Also, may badly organized countries stop blaming poverty and make sure they pay and support their teachers.

The problem with the lack of participation of these countries was that researchers lost a possible confirmation or disconfirmation of the IQ results obtained on those countries, which in the case of Africa seem to be too low to be believed. How to sort out this problem?

Internationally comparable test scores play a central role in both research and policy debates on education. However, the main international testing regimes, such as PISA, TIMSS, or PIRLS, include very few low-income countries. For instance, most countries in Southern and Eastern Africa have opted instead for a regional assessment known as SACMEQ. This paper exploits an overlap between the SACMEQ and TIMSS tests—in both country coverage, and questions asked— to assesses the feasibility of constructing global learning metrics by equating regional and international scales. I compare three different equating methods and find that learning levels in this sample of African countries are consistently (a) low in absolute terms, with average pupils scoring below the fifth percentile for most developed economies; (b) significantly lower than predicted by African per capita GDP levels; and (c) converging slowly, if at all, to the rest of the world during the 2000s. While these broad patterns are robust, average performance in individual countries is quite sensitive to the method chosen to link scores. Creating test scores which are truly internationally comparable would be a global public good, requiring more concerted effort at the design stage.

This fine paper comes from the economic sphere of study, so does not reference much psychometric literature. A pity, because it contributes much to the debate on group differences. Economists often ignore the concept of intelligence. Sandefur also seems to accept African national economic statistics, though he probably realizes they are prone to wishful thinking. The author is circumspect about the key issue of comparability of difficulty levels across tests, but seems to have made reasonable choices. I doubt that a re-working would change the picture very much.

The linkage is made possible by Botswana and South Africa having taken both the regional SACMEQ and the TIMSS international tests; and the 2000 and 2007 regional tests having used some of the TIMSS international test questions.

Whatever the linkage methods, the results are pretty grim:

Substantively, the results here are daunting for African education systems. Most of the national test-score averages I estimate for the thirteen African countries in my sample fall more than two standard deviations below the TIMSS average, which places them below the 5th percentile in most European, North American, and East Asian countries. In contrast, scores from the SACMEQ test administered to math teachers are much higher, but fall only modestly above the TIMSS sample average for seventh- and eighth-grade pupils, in line with earlier analysis by Spaull and van der Berg (2013). African test scores appear low relative to national GDP levels; in a regression of average scores on per capita GDP in PPP terms, average scores in the SACMEQ sample are significantly below the predicted value using all three linking methodologies. Furthermore, there is little sign that African scores were improving rapidly or converging to OECD levels during the 2000s.

Of course, readers of this blog will know that Richard Lynn’s personal collection of international intelligence test results, now in the Becker edition, puts Sub Saharan intelligence two standard deviations below the European mean, so it closely matches these results.

The advantage of using Maths tests as a proxy for intelligence tests is that most intelligence tests have an Arithmetic subtest and/or number series tests, so one can follow some known correlations to estimate comparability's. Better still, Maths has a logic to it, so it is valid to talk about some operations being more complex than others. The same item is very much the same item whichever test you find it in, because the same steps are required to solve it. It has the cold beauty of which Bertrand Russell spoke:

“Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry”.

More prosaically, maths opens the door to many other intellectual tasks, much as literacy supersedes the oral tradition.

What is to be done with African Maths teachers? Heiner Rindermann, trying to resolve the debate between Richard Lynn and Jelte Wicherts, put Sub-Saharan African IQ at 76. As to African Maths teachers’ results in this paper, he says: In some African countries teachers seem to have lower abilities than students in Europe or East-Asia!

If teachers are one standard deviation above the national mean, then they would have IQs of 91, if two standard deviations above the mean still only 106. This is not a level likely to inculcate in their students a passion for Maths, a subject which every schoolchild recognizes as being different conceptually from other language based subjects, and hard to master. What makes problems difficult? I digress.

Convergence is a much desired trajectory where racial differences are concerned. Put in the educational resources and the slower countries will catch up with the faster ones. Makes sense. However, this sought-after outcome does not always materialize. Convergence will take place sometime between 40 years and never, according to Woodley and Meisenberg.

Turning to the pressing issue of how to raise scholastic attainments, it is unlikely to be a simple question of investing money. Saudi Arabia has had plenty of money to spend on education for almost 50 years, and just look where it languishes in the table, in the company of far less wealthy Swaziland, Tanzania, Botswana and Uganda. Of course, given Saudi Arabia’s mean IQ of 78 that would be entirely as expected. No Africanist, I have nonetheless sung the praises of Botswana, a well run country which invests heavily in education (the Diamond Generation). Despite that, Botswana is not getting much bang for its buck. If Botswana cannot converge on other nations, despite having done so many things right, that should give pause for thought. Botswana’s mean IQ 73.

A summary of investment in education suggests that the pay-off is front-end loaded: the first $5000 has a big effect, and then it tends to plateau thereafter. Another way of looking at it is to note that once countries get to $16,000 GDP per capita then schooling in those countries accounts for only 10% of the variance of student attainment. So, poor countries (most of Africa is well below this level) should have plenty of scope for educational gains.

This paper completes a jigsaw puzzle, and extends the global scholastic attainment dataset by 14 countries. It confirms the Lynn assessments as likely to be correct, within a measurement error of roughly 4 IQ points. For these countries at least, it gives no hint of exceptional talents beyond that expected on the basis of intelligence testing.

I don’t do policy, so this is said more in hope than with any expectation of a good result, but if young Europeans school-leavers with good maths qualifications intending to do good works in Africa want to be most effective, instead of digging ditches they should concentrate on teaching Maths.

31 comments:

"If teachers are one standard deviation above the national mean, then they would have IQs of 91, if two standard deviations above the mean still only 106. This is not a level likely to inculcate in their students a passion for Maths": I wonder.

Is it possible that there might be a phenomenon whereby if a teacher is far cleverer than his pupils it can sometimes be a disadvantage? Could there be an optimal IQ gap? (Some sort of age-correction might be needed to make this question meaningful.) But maybe not, maybe the problem is far too intricate to be summarised by such a glib suggestion.

I wonder whether it could work the other way round late in Secondary School : if the pupil was cleverer than the teacher by too large a margin it might become harder for the teacher to succeed. Maybe that means that in Secondary Schools the cleverest teachers should generally teach the oldest and cleverest pupils. I shouldn't be surprised if schools learned this lesson millennia ago.

P.S. I'm not being negative. I dare say that your suggestion that gap-yah kids teach maths is a good one. The teachers' unions in Africa won't like it though.

I watched an excellent two hour documentary of a Chinese road building company in the Congo. It's main characters were two Chinese bosses and one African translator. The Chinese were both curious and surprisingly benevolent in regard to Africans as they are. The African spoke French, Chinese, and several African dialects. The unstated conclusion of the Chinese was that Africans are quite stupid but admirably well suited to the conditions in which they live, and I stress that they were in fact impressed that no other race could exist there without support. The African was indispensable not only for language but for informing the Chinese of vast cultural impediments to making normal contractual arrangements. Yet when it came to grasping ideas new or alien to him he shut down and his face became a total blank. No one will or can breach that chasm. Or should. Trying to accomplish was is inherently impossible causes damage all it's own.

What is puzzling is a non-standard disparity between pupils and teachers (p 44) in Kenya and, maybe, Seychelles.Do they employ their brightest as teachers, are the teachers clever enough to cheat or are the teachers from a specic sub population/tribe?

Math's is very important BUT the basis of thought is also extremely important, the basis, the origin of thought or anything is always important. Seems quite common that ''math-high achievers'' tend to believe they are gods because their talent in this area, of course, becoming irrational during the process.

The worst type of humantype is the arrogant and stubborn [cognitively] smart people because they on avg will be very good to ''rationalize'' their mistakes and they will be near to the power, and many times, full-in, to impose their irrational pre-conceptions, on the right, on the left, on the middle, etc...

Saudi Arabian per-capita GDP $53,600. They spend over 20% of per capita GDP on education per pupil according to http://data.worldbank.org/indicator/SE.XPD.TOTL.GB.ZS?locations=SA. United States spends something like 13%. Very revealing, since it tends to disentangle wealth and spending from educational level/development.

I think same thing... 78 IQ don't make sense. Would be interesting analyse the IQ scores of arabian ''nobility'' and political classes.

Qatar and Kwait seems very similar in collective behavior with Singapore. Ok, many foreigners living there, well, maybe ''we'' are analysing IQ scores of foreign people and not the native ones, supposedly the local elites.

Looking from the previous PISA mean score India is unlikely to have any space industry. With respect to the smart apexes or fractions the results are quite different.

The 2016 Int Math Olympiad rank for Saudi Arabia is 41 which is better than that for Poland, Switzerland and Netherlands. That for SouthAfrica is better than that for Estonia and Finland. That for Tunisia is better than that for Denmark. The results were obtained using exactly the same test materials, at the same time and place and conducted by the same organization. And by regulation the students must be the citizens of the countries concerned.

Since a math olympiad team is selected, you get to use the smart sub-populations. Thus South Africa has a substantial population of European descent, and can after selection furnish some decent candidates. So this sort of observation is silly.

How the hell is it silly? Tunisia and Saudi Arabia are monoethnic, at least for the purposes of this. Your comparison to the artificial and unique situation in South Africa is the only silly thing here.

Comparing the smart subpopulations of different ethnic groups is arguably even more important than comparing the the whole ethnic groups as those are the people that drive all the progress.

In some of those cases, it may have more to do with the size of population (like the huge Nigeria vs the tiny Luxembourg). But the cases Anonymous mentioned don't have those issues as they have comparable population sizes.

In a multimodal population, arguing from the scores of a few individuals, progressively winnowed from whoever happens to enter from the heterogeneous population, as the Math Olympiad is (there is actually no "sample" as such) is of no use whatsoever.

A quick look at Wikipedia gives this for immigrants in Saudi Arabia. You can be sure of strong selection for a substantial fraction of these people. Smewhere among them you can find decent entrants for the Olympiad, even if the mean IQ of Saudis is subterranean.

You have no idea what you're talking about with those foreign resident numbers. Even more so if you think that the selection for Indian/Paki/Bengali/Filipino immigrants is positive in Saudi Arabia is POSITIVE. If anything, it's very negative. You have no idea what the situation of foreign workers is in the gulf. The only groups with likely positive selection in your list are those from Middle Eastern or North African countries.

Moreover, your list is completely useless for the subject at hand. Almost none of those people have citizenship, will ever be able to acquire citizenship, nor will their children ever have citizenship. You're projecting western notions onto lands that don't care about them. Same applies to foreigners in China by the way.

Only citizens are able to compete for their home country in the IMO. The negligible amount of bona fide foreigners with a citizenship in KSA, and with kids the right age, is unlikely to ever an effect on anything. And you can see that by going to the IMO website, and seeing for yourself that the dozens of participants Saudi Arabia had for the IMO were all without exception ethnically Saudi.

You obviously have no idea what you're talking about. All their names are Arabic, and not only Arabic but specifically Saudi. No South Asian or East Asian or whatever else you think they are https://www.imo-official.org/country_individual_r.aspx?code=SAU

And it's quite easy to guess too without looking it up if you know anything about the immigration situation in Saudi Arabia.

Even if not a single team member had any immigrant ancestry whatever, this all tells you nothing beyond the fact that they have a large enough population to select out a few individuals (6 or so) who can put up a decent show at Math.

Assuming a unimodal population (for simplicity) with a mean IQ of say 85 and sdev of 15, there are about 3685 people with IQ > 140 if the population size is 30,000,000. Presumably more than enough to assemble 6 people for a decent Math Olympiad team.

Gavan, the population of Poland is 40 million, Spain's population is 50 million.

Besides, if you actually bother to do the math, you'll realize that this population difference doesn't mean shit with a full sd difference. Denmark, Norway, Estonia, Finland, Sweden, etc are all supposed to have more 140+ IQ people than Saudi Arabia, yet all trail behind it in the IMO.

You also have your horrible assumption that 140 is some magic cut off above which only practice counts. If that was the case, the US team wouldn't be almost all East Asian and Indian, and the South African team wouldn't be all white and Indian.

By the way, I hope you all realize that all the immigrants in Saudi Arabia stay for ever immigrants, and that includes their children as they inherit the parents' nationality. So yes, the distribution is fucking bimodal. Obviously societal strata exist, and the elite will outscore the poor, as everywhere else in the world; that doesn't make it polymodal.

Finally, your statement about the amount of people with an IQ of 140+ is stupid. The pool of possible candidates for IMO is incredibly limited, and if you try and calculate the sd of the participants, it will be around 2 years. You can at least restrict your population to those between 12 and 18.

I have no idea why you have to lard your comments with bluster like 'fucking', 'shit', 'horrible', 'stupid' etc. etc. Calm down.

As for Saudi Citizenship, I note that "A foreign woman who marries a Saudi man has right to citizenship provided that she gives up her foreign citizenship" although men would evidently find it a lot harder. That still leaves lots of room for injection of better genes at the elite level.

I didn't make any of the claims about "cutoff points" you ascribe to me, you inserted those yourself. It isn't hard to work out that in the qualifying age group the Saudis have easily enough people to yield a pool of a few decent candidates for the math olympiad. There will be other sources of variation that can easily account for the Saudis ranking higher than their average score suggests, with IQ nonetheless remaining influential, also noting that at the extremes IQ loses predictive power and normality will certainly be violated at the tails.

I also have no doubt that the real distribution is multimodal and that they have talented subpopulations, I said so at the beginning. All the more reason not to try and reason about the general Saudi population from a sliver of elite achievement, which was exactly my point. That's hardly a controversial point.

>I also have no doubt that the real distribution is multimodal and that they have talented subpopulations, I said so at the beginning. All the more reason not to try and reason about the general Saudi population from a sliver of elite achievement, which was exactly my point. That's hardly a controversial point.

I said the opposite. There is no reason to expect polymodality based on your premise.There are elite population everywhere, and yes endogamous ones (to varying degrees). Including the west. That doesn't really translate to polymodality on its own. Even more so because of assortative mating.

>I didn't make any of the claims about "cutoff points" you ascribe to me, you inserted those yourself. It isn't hard to work out that in the qualifying age group the Saudis have easily enough people to yield a pool of a few decent candidates for the math olympiad.

It's not exactly clear to me that among a couple hundred students with an IQ above 140 in Saudi Arabia, that there will also be enough that are very interested in mathematics and particularly excellent at it (not just best in class, which is rather easier). Have to remember here that the positive manifold for a very high IQ group is much weaker than for the general population (making g explain less of the variation).

As for the cutoff point subject, if the Saudi mean is 84, that means that the difference between western potential for say 160+ IQ (4sd for west, 5sd for Saudi. 5sd was good enough for the detection of the Higgs boson.) and Saudi potential for such IQ is insanely large, and the difference gets more dramatic the higher we go. That's why it isn't really obvious that Saudi Arabia would have a better aggregate score than all those western and northwestern European countries who are expected to have an appreciable number of super-geniuses, unlike Saudi Arabia.

There are good reasons for the higher results of Saudi Arabia, but IQ isn't one of them and that's really my whole point. The IQ of Romania is 90 (no, no gypsies), and their population is not that large (20m), yet they're one of the best performers at IMO. The reasons for that are similar to the reasons for Saudi Arabia, and they don't have to do with IQ.